Let vector u , v , and w be vectors such that vector u+v+w=0 if |u|=3, |v|=4 and |w| =5 then u.v+v.w+w.u=?

Answers (1)

Solution:    Since   vecu+vecv+vecw=0 , we have 

            left | vecu+vecv+vecw 
ight |^2=0\ \ Rightarrow hspace1cmleft | vecu 
ight |^2+left | vecv 
ight |^2+left | vecw 
ight |^2+2(vecucdot vecv+vecvcdot vecw+vecwcdot vecu)=0\ \ Rightarrow hspace1cm9+16+25+2(2(vecucdot vecv+vecvcdot vecw+vecwcdot vecu))=0\ \ Rightarrow hspace1cm(vecucdot vecv+vecvcdot vecw+vecwcdot vecu)=-25

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